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A key challenge for supporting elastic behaviour in cloud systems is to achieve a good performance in automated (de-)provisioning and scheduling of computing resources. One of the key aspects that can be significant is the overheads associated with deploying, terminating and maintaining resources. Therefore, due to their lower start up and termination overhead, containers are rapidly replacing Virtual Machines (VMs) in many cloud deployments, as the computation instance of choice. In this paper, we analyse the performance of Kubernetes achieved through a Petri net-based performance model. Kubernetes is a container management system for a distributed cluster environment. Our model can be characterised using data from a Kubernetes deployment, and can be exploited for supporting capacity planning and designing Kubernetes-based elastic applications.